Pseudo Sonic Article

8/12/2019 Pseudo Sonic Article

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TTecec hno logy Corhno logy Cor nerner

Introduction

The role of the synthetic seismo-gram(SS) as a supporting element ofprospect presentations involving seis-mic data is well established, as abridge between the domains of timeand depth it's functionality is essentialfor rigorous interpretation of a seismicprofile.

A SS for a well is computed from asonic log(DT) taken in the open bore-hole, with the bulk densitylog(RHOB) making a supplementalcontribution. Log curves, as discussed

here, are in the form of digital LogAscii Standard(LAS) files, a handy for-mat for loading, viewing and aug-menting well log data in a workstationenvironment. More information anduseful software for manipulating LASfiles are available at the website of theCanadian Well Logging Society(www.cwls.org).

Sonic Log to SyntheticSeismogram

The first step in computing a SS is to

integrate(sum the values) of the DTcurve in order to convert the log fromDT vs. depth to Interval Velocity(VI)vs. time, the resulting velocity valuesbeing equally spaced at discreet timeintervals, usually 1ms. This transformestablishes a time vs. depth relation-ship over the logged segment of thewell, the result being only as accurateas the DT curve. Since the DT curveseldom starts at the surface, or datumof the seismic, an estimate of the shal-low velocity is applied to establish the

seismic time at the start of the DT log.From the integrated log at discreet

time intervals, and an RHOB log ifavailable, reflection coefficients arecomputed which, when convolvedwith a suitable wavelet, will yield a SStrace. This trace, plotted at the correctdisplay scales, should resemble theseismic data at the well location. It isnot uncommon for stretching or

squeezing of the SS to be required toachieve a properly tied result.Reflection character matches betweenthe SS and the seismic data determinewhere adjustments are needed. Arefined SS will provide an accuratetime/depth function at the well tiepoint and positive identification ofgeologic horizons in the seismic data.It may also be used to model changesin lithology and fluid content in for-mations of interest.

Pseudo-Sonic LogsIt is often the case that wells near a

prospect had no sonic log run, havelarge gaps in the log, or was notreleased. Any of these situations cre-ate a need for an effective and accessi-ble method for computing an accuratepseudo-sonic(DTP). DTP being thename applied to an approximation ofa sonic log that is derived from a dif-ferent log type. An accurate DTP will

make a useful SS in the absence of aDT log. The DTP may also be used tofill gaps in a DT or to replace poorquality DT data zones.

References listed are a selection oftitles the reader may explore to appre-ciate the history of this field ofresearch. DTP algorithms are general-ly developed by the application ofnon-linear numerical analysis tech-niques to empirical data sets in theform of log cross-plots and may evokea glassy-eyed response.

In the absence of a DT log, whichnormally appears only on the detaildisplay of a sonic log, it is usually thecase that either an Induction log atcorrelation scale(1"/100') or aDensity/Neutron porosity log will beavailable. It is the purpose of this arti-cle to explore options for using theselog types for DTP calculation.

(Continued)

by Joe H. Smith, #1179, Petrophysics, Inc. Plano, Texas

Pseudo-sonics, Synthet ics and the Lay of the LandPseudo-sonics , Synthet ics and the Lay of the Land

Figure 1. Induction-Acoustic detail log over a sand interval in a Jim Hogg Co., TX well.Curves of interest from left to right are SP, Rild, Rsfl and DT (dashed).


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DTP From Resistivity Logs

A common method for DTP calcula-tion is to use Faust's Equation to calcu-late the pseudo-sonic from a resistivi-ty log. This algorithm is typicallyavailable in interpretation softwarepackages that have SS capability. The

algorithm is easy to use but often failsto give accurate results since it is a"one-size fits all" approach with limit-ed user control. The best geologic set-ting for using Faust's Equation arethose regions where velocity increasesuniformly with depth without abruptchanges in formation age or lithology,south Louisiana being an example.

Successful use of a resistivity log forDTP calculation starts with the deci-sion of which resistivity curve toemploy. With an induction log at1"/100' correlation scale one may onlyhave shallow(SFL or SN) and deep(ILD) curves to choose from. ConsiderFigure 1 (shown on page 29), a detaillog interval of Induction/Acousticfrom Jim Wells Co., TX. The curves ofinterest from left track are: SP(solid),middle track, ILD(long dash) andSFL(solid), and right track, DT(dash).Note that the SFL follows the charac-ter of the DT curve very closely acrossthe entire interval. The ILD, however,

diverges sharply at the sand begin-ning around 5354' and continues toread low values throughout the sandinterval. This phenomenon oftenoccurs when the well bore penetrateshigh porosity wet sands in a clasticsetting, the Gulf Coast onshore beingtypical. The deep induction log is "see-ing" a large volume of salt water in theporous sand and is recording theresistivity of the formation fluid. TheSFL, contrastly, is measuring in amuch smaller volume, near the path

the sound wave from the sonic logtravels. Observation suggests thatusing the ILD will create a much slow-er DTP in sands, resulting in a slowerintegrated DTP and a negative reflec-tion at the top of the sand whichshould be positive, leading to mis-cor-relation of the SS to the seismic data.This can be a source of significant DTPerror in wells where a high percentage

of thick, porous sands have beenlogged, as in the Miocene of the GulfCoast onshore.

Cross-Plot Technique

Cross-plots between the resistivi-ty(RS) and sonic(DT) logs in a pilotwell may be used to determine a scalefunction, or mathematical relation-ship, between the log types. The scalefunction may be applied to wells withthe same type RS log which are in asimilar geologic setting to calculate aDTP. Scale functions can be deter-mined in a depth varying fashionwith consideration to formation ageand lithology changes. This methodallows more refined control of thescale functions than does Faust'sEquation and often provides superior

results.The cross-plot data points are theaverage resistivity value associatedwith each DT value that occurs in aspecified depth interval of the pilotlog. It is informative to differentiatethe values by referencing a lithology

log at each data point to determine ifit was recorded in shale or sand. Thisallows scale function differences dueto lithology to be observed.

Figure 2 is a cross-plot between Rsfland DT in the Jim Wells Co. well inFigure 1. The sand interval is included

in the 600' cross-plot zone as indicatedby the depth range. This plot reveals anearly smooth relationship betweenthe Rsfl and DT in sand or shale, giv-ing confidence that a useable scalefunction can be obtained by fitting thedistribution on the cross-plot with aLeast Mean Square(LMS) polynomialIn this case a second order LMS func-tion like DTP = 93. - (Rsfl) * 90. +(Rsfl^2.) * 53 is a close fit. By repeat-ing the cross-plot along the range oflogged data a depth varying function

can be determined which can be usedto create an accurate DTP for nearbywells with a similar type RS curve. Aninventory of such functions for differ-ent areas can be a valuable addition tothe interpreter's toolkit.

(Continued)

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Technology orner ontinued

Figure 2. Cross-plot of DT vs. Rsfl over a log interval including Figure 1. Circles(o) representvalues taken in sand, plus (+) are values in shale based on the SP. This distribution can beused to determine an accurate scale function.


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Figure 3 is a cross-plot between ILDand DT over the same interval as thatin Figure 2. Note the separationbetween the values recorded in sandfrom those in shale. This plot confirmsstatistically what was observed inFigure 1 and suggests that a single

scale function cannot describe the ILDto DT relationship in this zone.

It is frequently the case that the SFL,in addition to being a more accuratesource curve for DTP calculation inclastics, is better behaved in high resis-tivity carbonates and delivers moreuseful data due to it's superior resolu-tion.

DTP from Density/Neutron Logs

Algorithms for computing velocityfrom RHOB logs are availableTypically a form of Gardner's equationwill be used, i.e., V= (RHOB/C)^4.,where RHOB is in g/cc, C=.23 and V isft/sec. This formula results in a fastervelocity with increased density, whichis counter to what is observed in aclastic section like the Gulf Coast,where lower density sands may befaster than high density shales.

Figure 4 is a cross-plot between theDT and RHOB curves over a 1000

interval of the Jim Wells, Co. well. Theshape of this data distribution isambiguous, inferring that an accurateDTP could not be derived from theRHOB curve. The sensitivity of thedensity log to borehole conditions isone of several factors suggesting itmay not be suitable for DTP calcula-tion. Other weaknesses of usingRHOB to calculate velocity are docu-mented in the literature.

Figure 5 (shown on page 32) is a

cross-plot between DT and NPHIcurves over the same interval asFigure 4 and reveals a nearly linearrelationship between these curves inthe subject well. This type of distribu-tion can be approximated with a scalefunction of the form DTP = A * NPHI+ B, where A is the slope of the curveand B is the DT axis intercept point. A

(Continued)


Figure 3. Cross-plot of DT vs. Rild over the same interval as Figure 2. The bifurcation of sandvalues from shale values suggest that a single scale function cannot be derived from thesedata points.

Figure 4. Cross-plot of DT vs. Rhob over a 1000 interval of the well in Figure 1. Note thatthe DT values associated with a density of 2.35 g/cc range from 110 to less than 90us/f.


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and B can be calculated by inspection

from the cross-plot. In the case abovevalues of A=1.65 and B=40. result in avery close fit to the distribution. Thistype of linear scale function betweenthe DT and NPHI has been observedin several mature basins and is reliablefor DTP calculation. Small adjust-ments in the slope and intercept areneeded in different areas but the lin-earity is a consistent feature of thisrelationship. Developing depth vari-ant functions in a pilot well is possibleusing spreadsheet type software andthe DT vs. NPHI relationship.

Caveats

The presence of hydrocarbons in theformations logged will distort theresults of either of the methods for cal-culating the DTP that have beendescribed. It is necessary to manuallyedit those zones where gas effect ispresent in the NPHI values or hydro-

carbon resistivity in the RS curves.

This is normally handled by referringto a wet zone of comparable lithologyand adjusting the DTP values tomodel the conditions present. Wyllie'sequations are useful for making thesemodifications.

Modern full-array resistivity logs arerecorded using multiple transducersof varying length and depth of inves-tigation, the data are combined, ormixed, in a fashion not known to thecustomer, a result being that the qual-ities of the short investigation tool thatare useful for DTP calculation in olderlogs are diminished in newer ones.Given a choice of using a contempo-rary full array log or an eighties vin-tage induction log to compute a DTPthe later is the better option.

Conclusions

Calculating an accurate DTP is notalways an easy task but can be accom-plished with patience and attention tothe limitations of the log types avail-able to use.

In the case of resistivity logs, a shal-low investigation curve type is superi-or to the deep for this purpose.

A custom designed, depth varyingscale function that considers forma-tion age boundaries will yield moreaccruate results than a general pur-pose algorithm.

The neutron log is a superior optionto the bulk density log for calculatinga DTP when only a porosity log isavailable.

References

Burch, D., March 2002, Sonic LogsNeed Troubleshooting: AAPGExplorer/Geophysical Corner

Faust, L.Y., 1951, A Velocity FunctionIncluding Lithogic VariationGeophysics, v. 18, No. 2, p. 271-288.

Rudman, A.J., et al, 1975,Transformation of Resistivity Logs toPseudovelocity Logs: AAPG Bulletin,v. 59, No. 7, p. 1151-1165.

Wyllie, M.R.J., et al, 1958, AnExperimental Investigation of FactorsAffecting Elastic Wave Velocities inPorous Media: Geophysics, v. 23, p.459-493.

Joe H. Smith is anindependent consult-ing geophysicist andcan be reached atj s m i t h @ p e t r o -

physics.com

If you have a Technology Corner articlethat you would like to submit forpublication in the SIPES Quarterly, pleaseemail it to Dick Cleveland at [email protected].


Figure 5. Cross-plot of DT vs. Nphi over the same interval as Figure 3. In this case a nearlinear distribution of points makes a simple and accurate scale function possible.

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